摘要: this article is assisted by Deepseek, asked free version chatgpt got time out multiple times. Combined errors of running 'inference' LLM example bound by electronic limits.
Total System ~0.001–1 Mostly corrected; worst case → wrong output.



Can you estimate each day on the earth in computer industry? how many times and size of data read from and written to volatile media (eg. memory), and non-volatile memory eg ssd/harddisk. Then estimate the total errors and rate of errors. So we will se a table with eigtht columns, read from memory size, read from memory overall error rate, write to memory size, ...



Estimating the daily data movements and error rates in the computer industry is challenging due to the vast scale and diversity of systems. However, we can create a rough approximation based on available data and reasonable assumptions. Here's a structured breakdown:
Key Assumptions & Data Sources:

Global Data Traffic (Memory/Storage):

Memory (DRAM): Estimates suggest billions of terabytes (TB) are processed daily in memory.

Storage (SSD/HDD): Global data storage traffic is in the exabytes (EB) per day.

Error rates are based on industry standards (e.g., DRAM error rates ~1e-12 to 1e-15, SSD/HDD error rates ~1e-15 to 1e-16).

Error Rates:

DRAM: Soft error rate ~1e-12 per bit (varies with technology).

SSD/HDD: Unrecoverable read errors ~1e-15 per bit (SSD) to 1e-16 (enterprise HDD).

Daily Activity:

Memory read/write operations are orders of magnitude higher than storage due to caching.

Storage writes are less frequent but involve larger blocks.

Estimated Daily Data Movements & Errors
Category Read Size (per day) Read Error Rate Write Size (per day) Write Error Rate Total Errors (Read) Total Errors (Write) Overall Error Rate
Volatile (DRAM) ~10-100 exabytes (EB) ~1e-12 per bit ~10-100 EB ~1e-12 per bit ~10-100 million ~10-100 million ~1e-12
Non-Volatile (SSD/HDD) ~1-10 exabytes (EB) ~1e-15 per bit ~0.1-1 EB ~1e-15 per bit ~1-10 thousand ~0.1-1 thousand ~1e-15
Breakdown of Estimates:

DRAM (Memory):

Read/Write Size: Assuming ~100 billion devices (servers, PCs, phones) each handling ~1-10 GB/day → 10-100 EB/day.

Errors: At 1e-12 error rate → 10-100 million errors/day (mostly corrected by ECC).

SSD/HDD (Storage):

Read Size: Cloud/enterprise storage handles ~1-10 EB/day (e.g., AWS S3 serves trillions of requests daily).

Write Size: Slower due to writes being buffered in memory first (~0.1-1 EB/day).

Errors: At 1e-15 error rate → ~1,000-10,000 read errors/day globally (most handled by RAID/retries).

Notes:

Error Mitigation: Most errors are corrected via ECC (DRAM), RAID (storage), or retries.

Variability: Estimates vary by workload (e.g., AI/ML clusters have higher memory traffic).

Future Trends: Error rates improve with newer tech (e.g., LPDDR5, QLC SSDs), but data volumes grow faster.

This table provides a high-order approximation; real-world numbers depend on specific infrastructure and workloads.
Let's try another scenario, for Deepseek example 'inference', I remember it is performed in the GPU, calculated the GPU errors, and network errors, also analyze other infrastructure introduced errors, and combined effect.

To analyze the error landscape for DeepSeek inference, we need to consider errors introduced at different stages of the pipeline:

GPU Computation (e.g., matrix multiplications, attention mechanisms)

Network Transmission (e.g., data movement between GPUs/nodes)

Memory/Storage Errors (e.g., DRAM, HBM, SSD reads/writes)

Software/System-Level Errors (e.g., quantization, driver bugs)

We’ll estimate error rates, impact, and mitigation strategies for each component.
1. GPU Computation Errors

Sources:

Transient (Soft) Errors: Cosmic rays, voltage fluctuations → bit flips in registers/SRAM.

Permanent (Hard) Errors: Silicon degradation, electromigration.

Numerical Errors: Floating-point rounding (FP16/FP32/BF16).

Error Rates (Approx.):
Component Error Rate Example Impact
GPU ALU (FP ops) ~1e-9 to 1e-12 per op Incorrect attention scores, logits.
GPU SRAM (Cache) ~1e-10 to 1e-13 per bit Wrong weights loaded in matmul.
HBM (DRAM) ~1e-12 to 1e-15 per bit Faulty KV cache in transformer layers.

Mitigation:

ECC Memory: Corrects single-bit, detects double-bit errors (HBM).

Algorithmic Resilience: Gradient clipping, redundant computation checks.

2. Network Transmission Errors

Sources:

Data Corruption: Packet drops, bit flips (InfiniBand/Ethernet).

Latency Jitter: Synchronization issues in distributed inference.

Error Rates:
Network Type Bit Error Rate (BER) Impact
InfiniBand (RDMA) ~1e-15 to 1e-18 Rare, but catastrophic if uncorrected.
Ethernet ~1e-12 to 1e-15 More likely in large-scale deployments.

Mitigation:

CRC Checksums: Detects/corrects errors in packets.

Retransmission Protocols: TCP/IP retries corrupted data.

3. Memory/Storage Errors

Sources:

DRAM/HBM Bit Flips: Row hammer, thermal noise.

SSD/HDD Read Errors: NAND wear-out, controller bugs.

Error Rates:
Medium Error Rate Example Impact
HBM ~1e-12 to 1e-15/bit Incorrect weight fetches.
SSD ~1e-15 to 1e-16/bit Faulty model checkpoint loads.

Mitigation:

ECC + RAID: Protects against uncorrectable errors.

Checksumming: Detects silent data corruption.

4. Software/System-Level Errors

Sources:

Quantization Errors: FP16 → INT8 conversion noise.

Kernel Bugs: CUDA driver inaccuracies.

Synchronization Issues: Race conditions in multi-GPU inference.

Error Rates:

Quantization Noise: ~0.1%–1% perplexity increase (model-dependent).

Software Bugs: Hard to quantify (varies by implementation).

Mitigation:

Numerical Stability Checks: Gradient scaling, NaN detection.

Redundant Execution: Compare outputs across GPU replicas.

Combined Effect in DeepSeek Inference

Assuming:

1,000 A100 GPUs running inference on 7B-parameter model.

Per-GPU workload: ~100 GB HBM traffic, ~1e12 FLOPs per query.

Component Errors per Query Impact
GPU Computation ~0.001–1 (FP errors) Minor logit deviation.
HBM (DRAM) ~0.0001–0.01 Rare weight corruption (if no ECC).
Network ~1e-6–1e-9 Almost negligible (with RDMA/CRC).
Total System ~0.001–1 Mostly corrected; worst case → wrong output.
Conclusion

Most errors are masked by ECC, checksums, and algorithmic robustness.

Worst-case scenarios: Silent corruption → rare hallucinations or incorrect responses.

Mitigation:

Use ECC-enabled GPUs (NVIDIA A100/H100).

Validate outputs via checksumming (e.g., comparing inference runs).

Monitor hardware logs for correctable errors (predictive maintenance).

Would you like a deeper dive into any specific part (e.g., GPU fault injection studies)?

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